Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 57, 2009 - Issue 5: Special Issue on The Numerical Range and Numerical Radius
Submit an article Journal homepage
76
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Pfaffian and decomposable numerical range of a complex skew symmetric matrix

Wai-Shun Cheung Department of Mathematics and Statistics, Auburn University, AL 36849–5310, USA
&
Tin-Yau Tam Department of Mathematics and Statistics, Auburn University, AL 36849–5310, USACorrespondence[email protected]
Pages 477-489 | Received 02 Dec 2008, Accepted 02 Mar 2009, Published online: 22 Jun 2009

References

  • Brickman , L . 1961 . On the field of values of a matrix . Proc. Am. Math. Soc. , 12 : 61 – 66 .
  • Cheung , WS and Tam , TY . 2008 . The K-orbit of a normal element in a complex semisimple Lie algebra . Pacific J. Math. , 238 : 387 – 398 .
  • W.S. Cheung and T.Y. Tam, Star-shapedness and K-orbits in complex semisimple Lie algebras, to appear in Bull. Canad. Math. Soc
  • Cheung , WS and Tsing , NK . 1996 . The C-numerical range of matrices is star-shaped . Lin. Multilin. Alg. , 41 : 245 – 250 .
  • Choi , MD , Laurie , C , Radjavi , H and Rosenthal , P . 1987 . On the congruence numerical range and related functions of matrices . Lin. Multilin. Alg. , 22 : 1 – 5 .
  • Godsil , CD . 1993 . Algebraic Combinatorics , New York : CRC Press .
  • Hausdorff , F . 1919 . Der Wertvorrat einer Bilinearform . Math. Z. , 3 : 314 – 316 .
  • Horn , RA and Johnson , CR . 1991 . Topics in Matrix Analysis , Cambridge, , UK : Cambridge University Press .
  • Kasteleyn , PW . 1961 . The statistics of dimmers on a lattice . Physica , 27 : 1209 – 1225 .
  • Marcus , M . 1972/73 . Derivations, Plücker relations, and the numerical range . Indiana Univ. Math. J. , 22 : 1137 – 1149 .
  • Marcus , M and Filippenko , I . 1979 . Linear operators preserving the decomposable numerical range . Lin. Multilin. Alg. , 7 : 27 – 36 .
  • McIntosh , A . 1978 . The Toeplitz-Hausdorff theorem and ellipticity conditions . Amer. Math. Monthly , 85 : 475 – 477 .
  • Raghavendran , R . 1969 . Toeplitz–Hausdorff theorem on numerical ranges . Proc. Am. Math. Soc. , 20 : 284 – 285 .
  • Tam , TY . 1991 . Another proof of a result of Marcus without Plücker relations . Lin. Multilin. Alg. , 29 : 313 – 314 .
  • Tam , TY . 1999 . An extension of a convexity theorem of the generalized numerical range associated with SO (2n + 1) . Proc. Am. Math. Soc. , 127 : 35 – 44 .
  • Tam , TY . 2001 . Convexity of generalized numerical range associated with a compact Lie group . J. Aust. Math. Soc. , 71 : 1 – 10 .
  • Tsing , NK . 1981 . On the shape of the generalized numerical ranges . Lin. Multilin. Alg. , 10 : 173 – 182 .
  • Tutte , WT . 1947 . The factorization of linear graphs . J. London Math. Soc. , 22 : 107 – 111 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.